Given the following data set, the first thing that we need to do is come up with a scatter diagram. I did this and excel, and with this we get the following plot. So what we need to do with this has come up with a label to describe the relationship between the two variables and on the horizontal access we have the percent of, um, working and on the why we have the percent of management. And because we see that as the percent of working increases, um, our percent of management increases. You can say that there is a positive relationship and because our if we draw we drew a line of best fit through this and you had a better artist, you could see that the relationship between these two variables is linear. So what that means is, as our X variable increases or by why variable increases at a constant rate. So this would be a positive linear relationship. And now with this, we have to come up with a on estimated regression equation. So in order to come up with their estimated rigor regression equation, we will use this formula. So beta subzero zehr Arab on, beta. Someone is our, um our model, basically. And in order to find these variables, we need to use the following formula. So beta sub one is equal to the sum of each individual X value of minus the mean of the excess times each individual. Why value minus the mean of the wise over some of the differences between the X variable squared. So let's come up with these values. So first thing when you do is come up with X bar. An expert is just the the average of these values up here. So 67 plus 45 plus 73 plus 54 plus 61 divided by five, which is equal to 60. And now we'll do the same thing for why bar, except with, um, the bottom column over here. So 49 plus 21 for 65 plus 47 plus 33 divided by five is equal 2 43 And now we can just plug ah, the values in for the most part. So I'll just give you guys an example of this difference. This difference. And, um, just one of the square differences. So an individual X value minus, the X bar would be equal to 67 minus our exports. 60 67 minus 60 is equal to seven. And now you would take this kind of difference and do it for each of the variables would be 45 minus 60 plus 73 minus 60 54 minus 60 plus 61 minus 60. And then you do that for all of them and then the same thing for the y values. So you take an individual, why value and subtract the mean from it. So our y mean is 43. So 49 minus 43 is equal to six. And now you do this for the rest of the Y values, and then you would plug it into this formula up here. So ultimately, in the end, we will get 624. Do some different color 624 over the sum of our differences and X squared, which is for 80. We get a value of 1.3. So we have our beta one and now we need to come up with a beta subzero. This is the following in the following is the formula for our beta subzero, And that is simply the mean of the wide variable, minus the basis of one value times the mean of the xperia ble. We found the y. I mean to be 43 minus our basis of one which we found to be 1.3 and our ex mean, which is 60. And once we do this, we get a beta subzero value of negative 35. So we get, um, ultimately our estimated regression equation, which is the answer to Part D. That why hat is equal to negative 35 plus 1.3 X. Now, we can use this formula to come up with when, um uh Or what percent of management jobs helped a woman in a company that has 60% of women employees. So what we have to do is just, ah, plug in 60 wherever we see X. And we do that as like we do in this formula over here, and we get a value Ah, 43%